Lab 3

Univariate Linear Regression on Diabetes Dataset

Imported Data

array([[ 0.03807591,  0.05068012,  0.06169621, ..., -0.00259226,
         0.01990749, -0.01764613],
       [-0.00188202, -0.04464164, -0.05147406, ..., -0.03949338,
        -0.06833155, -0.09220405],
       [ 0.08529891,  0.05068012,  0.04445121, ..., -0.00259226,
         0.00286131, -0.02593034],
       ...,
       [ 0.04170844,  0.05068012, -0.01590626, ..., -0.01107952,
        -0.04688253,  0.01549073],
       [-0.04547248, -0.04464164,  0.03906215, ...,  0.02655962,
         0.04452873, -0.02593034],
       [-0.04547248, -0.04464164, -0.0730303 , ..., -0.03949338,
        -0.00422151,  0.00306441]])

(442, 10)

(442,)

Convert Diabetes X and show into table form using pandas

	age	sex	bmi	average_bp	S1_cholestrol	low_dl	high_dl	HD	ltg	glu
0	0.038076	0.050680	0.061696	0.021872	-0.044223	-0.034821	-0.043401	-0.002592	0.019907	-0.017646
1	-0.001882	-0.044642	-0.051474	-0.026328	-0.008449	-0.019163	0.074412	-0.039493	-0.068332	-0.092204
2	0.085299	0.050680	0.044451	-0.005670	-0.045599	-0.034194	-0.032356	-0.002592	0.002861	-0.025930
3	-0.089063	-0.044642	-0.011595	-0.036656	0.012191	0.024991	-0.036038	0.034309	0.022688	-0.009362
4	0.005383	-0.044642	-0.036385	0.021872	0.003935	0.015596	0.008142	-0.002592	-0.031988	-0.046641

Diabetes data head is shown in above figure.

Now change diabetes y into pandas table form and add with x table.

	progression
0	151.0
1	75.0
2	141.0
3	206.0
4	135.0

	age	sex	bmi	average_bp	S1_cholestrol	low_dl	high_dl	HD	ltg	glu	progression
0	0.038076	0.050680	0.061696	0.021872	-0.044223	-0.034821	-0.043401	-0.002592	0.019907	-0.017646	151.0
1	-0.001882	-0.044642	-0.051474	-0.026328	-0.008449	-0.019163	0.074412	-0.039493	-0.068332	-0.092204	75.0
2	0.085299	0.050680	0.044451	-0.005670	-0.045599	-0.034194	-0.032356	-0.002592	0.002861	-0.025930	141.0
3	-0.089063	-0.044642	-0.011595	-0.036656	0.012191	0.024991	-0.036038	0.034309	0.022688	-0.009362	206.0
4	0.005383	-0.044642	-0.036385	0.021872	0.003935	0.015596	0.008142	-0.002592	-0.031988	-0.046641	135.0

Visualization using Matplotlib

From the above graph we can see that progression of diabetes is higher for people who have high bmi and also people are who are old.

Univariate Linear Regression Model Building

Linear regression model for Body mass index feature and progression

Coefficients and intercepts

LinearRegression()

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Coefficients:  [981.65543614]
Intercept:  152.28824927379569

Slope is 981.65 which means model has positive correlation and the value where it intercepts is 152.2882

	Actual	Predicted
362	321.0	255.174269
249	215.0	211.794626
271	127.0	161.008702
435	64.0	129.267499
400	175.0	196.982065

Presenting the solution

Mean Absolute Error:  52.94370285288119
Mean Squared Error:  4150.6801893299835
Root Mean Squared Error:  64.42577271038341
R2 Score:  0.19057346847560142

In this model as we can see that mean absoulte error is high it means it is not giving accurate predicitions, moreover we have only selected one dependant variable. furthermore root mean squared error also shows that quality of predicitons are not good and they are too far from the true values measured.